Solve the inequality. Graph the solution. vert (x+8)/(3)vert -3gt 6 Select the correct choice below and, if necessary,fill in the answer boxes to complete your choice. A. xlt square or xgt square B. square lt xlt square C. The solution is all real numbers. D. There is no solution

To solve the inequality $\vert \frac {x+8}{3}\vert -3\gt 6$, we first isolate the absolute value expression by adding 3 to both sides of the inequality:<br /><br />$\vert \frac {x+8}{3}\vert \gt 9$<br /><br />Next, we split the inequality into two separate inequalities based on the definition of absolute value:<br /><br />$\frac {x+8}{3}\gt 9$ or $\frac {x+8}{3}\lt -9$<br /><br />Now, we solve each inequality separately:<br /><br />For $\frac {x+8}{3}\gt 9$, we multiply both sides by 3:<br /><br />$x+8\gt 27$<br /><br />Subtracting 8 from both sides gives:<br /><br />$x\gt 19$<br /><br />For $\frac {x+8}{3}\lt -9$, we multiply both sides by 3:<br /><br />$x+8\lt -27$<br /><br />Subtracting 8 from both sides gives:<br /><br />$x\lt -35$<br /><br />Therefore, the solution to the inequality is $x\lt -35$ or $x\gt 19$. The correct choice is A.